Joint State and Time-Varying Noise Variance Estimation in State-Space Models
Abstract
Reliable prediction from sequential data requires adaptation to changes in both the underlying dynamics and the accuracy of observations. These sources of variability have different implications: increased process variation necessitates faster adaptation, while increased observation noise requires greater caution in assimilating new measurements. We propose a recursive method to jointly estimate latent states and time-varying noise variances within state-space models. The method represents noise amplitudes as evolving latent variables and combines conditional Gaussian updates to account for uncertainty in these amplitudes and their dependence on the state. It accommodates direction-specific changes in process variation and, for Gaussian observations, simultaneous changes in observation variance. A scalar likelihood approximation extends process-variance learning to count-observations while preserving the count model for prediction. The procedure processes observations sequentially without repeatedly fitting past trajectories. Simulation studies involving persistent and transient changes illustrate how the method adapts to different sources of variability. Compared with fitted constant-variance alternatives, it enhances state estimation and predictive scores in the examined settings, while revealing the delay and attenuation that persist when tracking changing variances.
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BibTeX
@misc{mahoromeza2026joint,
title = {{Joint State and Time-Varying Noise Variance Estimation in State-Space Models}},
author = {Jean-Luc Mahoromeza and Olivier Wintenberger and Joseph De Vilmarest},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05778080v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Joint State and Time-Varying Noise Variance Estimation in State-Space Models
AU - Jean-Luc Mahoromeza
AU - Olivier Wintenberger
AU - Joseph De Vilmarest
PY - 2026
DA - 2026/10/05
PB - HAL
UR - https://hal.science/hal-05778080v1
AB - Reliable prediction from sequential data requires adaptation to changes in both the underlying dynamics and the accuracy of observations. These sources of variability have different implications: increased process variation necessitates faster adaptation, while increased observation noise requires greater caution in assimilating new measurements. We propose a recursive method to jointly estimate latent states and time-varying noise variances within state-space models. The method represents noise amplitudes as evolving latent variables and combines conditional Gaussian updates to account for uncertainty in these amplitudes and their dependence on the state. It accommodates direction-specific changes in process variation and, for Gaussian observations, simultaneous changes in observation variance. A scalar likelihood approximation extends process-variance learning to count-observations while preserving the count model for prediction. The procedure processes observations sequentially without repeatedly fitting past trajectories. Simulation studies involving persistent and transient changes illustrate how the method adapts to different sources of variability. Compared with fitted constant-variance alternatives, it enhances state estimation and predictive scores in the examined settings, while revealing the delay and attenuation that persist when tracking changing variances.
ER -